Dualities in dense quark matter with isospin, chiral, and chiral isospin imbalance in the framework of the large-Nc limit of the NJL4 model

In this paper, we investigate the phase structure of the dense quark matter in the presence of baryon μB, isospin μI, chiral μ5, and chiral isospin μI5 chemical potentials in the framework of the Nambu–Jona-Lasinio model. We show that, in the large-Nc limit (Nc is the number of quark colors), there exist three duality correspondences in the model. The first duality is between the chiral symmetry breaking and the charged-pion condensation phenomena, and there are two new dualities that hold only for chiral symmetry breaking and charged-pion condensation phenomena separately. These dualities show that chiral symmetry breaking phenomenon does not feel the difference between chiral μ5 and chiral isospin μI5 chemical potentials, and charged-pion condensation phenomenon does not feel the difference between isospin μI and chiral μ5 chemical potentials. We show that μ5 can generate charged-pion condensation, but this generation occurs at not so large baryon densities. In the case of both chiral imbalances (chiral μ5 and chiral isospin μI5 chemical potentials), the phase portrait is rather rich, and we show that charged-pion condensation in dense quark matter takes up a large part of the phase diagram. Charged-pion condensation in dense quark matter happens even in the case of zero isospin imbalance and requires only chiral imbalances; this fact can be demonstrated with the use of one of the new dualities and this is only one example of when these dualities are of great use in exploring the phase diagram.